He serves as the Member of Parliament for Kisoro Municipality, representing the National Resistance Movement (NRM), Uganda's ruling political party.

In 1991, he acquired a Grade 3 Certificate from Kisoro Primary Teachers' College (PTC), before attending Kyambogo University, where he attained a Diploma in Education in the year 2004.

Byibesho further advanced to Uganda Martyrs University Nkozi where he was a coordinator for Kisoro Students Association and graduated with a Bachelor of Education in 2009.

In 1997, when Resistance Councils (RCs) were renamed Local Councils (LCs), he continued to serve as an LC II chairperson for North Ward Parish, Kisoro TC Sub-county up until 2002 when he became the LC III Chairman, a position he held for 14 years.

In the later days of his LC III chairmanship, Byibesho bid for the more lucrative position of member of parliament on the NRM ticket and won both the party's 2015 primary elections and the 2016 general elections, thereby becoming a member of the 10th Parliament for the Pearl of Africa, representing Kisoro Municipality, Kisoro District.